| Process | Value | Uncertainty |
|---|---|---|
| Constant factor | \(z = A x ,\) with \(A\) a constant |
\(\Delta z = A\Delta x \) |
| Addition / Subtraction | \(z = Ax ± By,\) with \(A, B\) constants |
\(\Delta z = \sqrt{A^2\left(\Delta x\right)^2+B^2\left(\Delta y\right)^2} \) |
| Multiplication / Division | \(z = x\times y\) or \(z = \dfrac{x }{ y}\) | \(\Delta z = z\sqrt{\left(\dfrac{\Delta x}{x}\right)^2+\left(\dfrac{\Delta y}{y}\right)^2}\) |
| Function | \(f(x)\) | \(\Delta f = \left|\dfrac{d f}{d x}\right|\Delta x\) |
| Multi-variable unction | \(f\left(x_1,x_2,\cdots, x_n\right)\) | \(\ds \Delta f=\sqrt{\sum_{i=1}^{n}\left(\dfrac{\partial f(x) }{\partial x_i}\Delta x_i\right)^2}\) |